QMC Working Group VII: Multivariate Decomposition Method (MDM) and Applications

Group Leader:
Dirk Nuyens (KU Leuven – Belgium)
Alec Gilbert (University of New South Wales Sydney, Australia)

The multivariate decomposition method allows us to approximate infinite-dimensional problems by a sum of finite-dimensional subproblems in the “active set” whose size depends on the requested error demand. The weight structure imposed on these finite-dimensional subspaces often implies that the maximum number of variables in each subspace grows very slowly in terms of the requested error demand. Thus we only need to solve many low-dimensional problems (say, 1, 2, 3 dimensional) and a few medium-dimensional problems (say, up to 10 dimensions) to reach a reasonable error demand. These problems can be solved in parallel. The working group will develop efficient implementation of the MDM and consider its application to PDE problems with random coefficients as well as other potential applications.

News and Updates: Coming soon…

SAMSI Directorate Liaison: Ilse Ipsen

Questions: email qmc@samsi.info

Program on Quasi-Monte Carlo and High-Dimensional Sampling Methods for Applied Mathematics (QMC)